Well, first off there could have been more than one helicopter... I guess it depends on how big the helicopter really is supposed to be.
In Sue's letter she says "Prof. Booster was on our helicopter, and so was my mother, my brother, various assistants... The Doctor as well. He was there to serve our medical needs, and did so... At least, until he found the Demon Crown..."
Sue specify's "our" helicopter. Which might not mean anything or, it could mean there were more than one to begin with.
Also I don't think the Doctor just waltzed out of the chopper and said HAHAHA I WIN *nabs crown.* ....
EDIT: Oh it sounds like the scientists had been there for a bit before the Doctor finds the Crown... He was there to serve our medical needs, and did so... At least until blah etc, it makes little sense that Sue would have phrased it like that if the Doctor finds the Crown immediately.
For one, I don't think they originally landed the helicopter there, although it's possible, I find it unlikely. They don't even have any research equipment around, a base camp, or some place to sleep. There's nothing conclusive about this since it IS the intro, but when the Doctor finds the Crown it's as if the place is buried, or at least in total darkness. Maybe that makes more sense? The place could have been buried initally? Then when he finds the Crown, it causes the place to unbury or something? And at the end when the sky is raining Boulders from Heaven. Maybe it's more of the place being reburied.
There's also a chance that there is a second throne room somewhere in the deep that is based on or has the same layout as the original throne room. Seems unlikely, but not very unplausible for a variety of explanations.
Momorin and Itoh definitely use the rocket though. Seriously. They wouldn't waste days constructing a rocket just for a one time use for Quote, especially if they had another way to get to the surface. What's the deal with Last Cave? Perhaps there are multiple paths to the cave. A left path, middle path, and right path... Of course instead of having multiple doors, certain conditions are made before you take a different path. Either that or it's due to magic or the evil that's close by.
Speaking of evil, the only two places that the Black Wind Blows or something, is in Hell and in the Hard final cave. Which means there could be air coming from Hell or a passage or crack that connects to hell in that cave somewhere.
Why don't the humans get pwned by monsters and stuff? Well unlike Rambo (Quote), I think they take caution and sneak around; while Quote just runs up to everything and blows it up.
Most creatures can probably be avoided as in Sue's case. Kind of like walking past a wasp's nest, instead of going around shouting at and shaking the nest lol
Or walking through the jungle silently, as opposed to carrying around a machinegun shooting randomly around enemy territory...